Set Of Benchmark Problems Research Articles

Continuous-Energy Time-Dependent Coarse Mesh Transport (COMET) Method for Kinetics Calculations

In this paper, the novel continuous-energy coarse mesh transport (COMET) method is extended to perform time-dependent neutronics calculations in highly heterogeneous reactor core problems. In this method, the time-dependent transport equation is converted into a series of steady-state transport equations by estimating the time derivative term using implicit finite differencing. The resulting steady-state transport equations, having additional terms that are imbedded in the total collision term and in the volumetric source terms, are then solved by the steady-state COMET method, in which all the phase-space variables, including energy, are treated continuously. Finally, the fission density distribution constructed by the steady-state COMET is used to solve a set of ordinary differential equations to obtain the delayed neutron precursor concentrations. The time-dependent COMET method is benchmarked against a direct continuous-energy Monte Carlo method (i.e., MCNP) in a set of infinite homogeneous problems and a set of single-assembly benchmark problems consisting of identical pin cells. It is found that the COMET results agree very well with the Monte Carlo reference solutions while maintaining its formidable computational speed (orders of magnitude faster than the Monte Carlo method).

Progressive Learning Hill Climbing Algorithm with Energy-Map-Based Initialization for Image Reconstruction.

Image reconstruction is an interesting yet challenging optimization problem that has several potential applications. The task is to reconstruct an image using a fixed number of transparent polygons. Traditional gradient-based algorithms cannot be applied to the problem since the optimization objective has no explicit expression and cannot be represented by computational graphs. Metaheuristic search algorithms are powerful optimization techniques for solving complex optimization problems, especially in the context of incomplete information or limited computational capability. In this paper, we developed a novel metaheuristic search algorithm named progressive learning hill climbing (ProHC) for image reconstruction. Instead of placing all the polygons on a blank canvas at once, ProHC starts from one polygon and gradually adds new polygons to the canvas until reaching the number limit. Furthermore, an energy-map-based initialization operator was designed to facilitate the generation of new solutions. To assess the performance of the proposed algorithm, we constructed a benchmark problem set containing four different types of images. The experimental results demonstrated that ProHC was able to produce visually pleasing reconstructions of the benchmark images. Moreover, the time consumed by ProHC was much shorter than that of the existing approach.

On Nonstationary Gaussian Process Model for Solving Data-Driven Optimization Problems.

In data-driven evolutionary optimization, most existing Gaussian processes (GPs)-assisted evolutionary algorithms (EAs) adopt stationary GPs (SGPs) as surrogate models, which might be insufficient for solving most optimization problems. This article finds that GPs in the optimization problems are nonstationary with great probability. We propose to employ a nonstationary GP (NSGP) surrogate model for data-driven evolutionary optimization, where the mean of the NSGP is allowed to vary with the decision variables, while its residue variance follows an SGP. In this article, the nonstationarity of GPs in the tested functions is theoretically analyzed. In addition, this article constructs an NSGP where the SGP is a degenerate case. Performance comparisons of the NSGP with the SGP and the NSGP-assisted EA (NSGP-MAEA) with the SGP-assisted EA (SGP-MAEA) are carried out on a set of benchmark problems and an antenna design problem. These comparison results demonstrate the competitiveness of the NSGP model.

Integration of Three Vehicle Fleet Types for Delivering Relief Supplies During a Natural Disaster

The combined use of trucks and drones in last-mile delivery offers a more efficient and faster way to make deliveries from an operational standpoint. In this paper, we propose a new routing model that combines different vehicle fleets, including hybrid trucks, traditional trucks, and large drones, to deliver packages from a depot to different destinations cooperatively. This research will give us a better understanding of this drone logistics application, particularly in routing optimization. It can be further implemented to mitigate the impacts of natural disasters, mainly earthquakes, flooding, and landslides. This research aims to study the possibility of using drones to deliver relief supplies such as food, water, and medicine for humanitarian purposes during natural disaster periods to find the best possible route to directly reach the destination and minimize the flying time in the air. We develop a Mixed Integer Programming (MIP) formulation to solve the I-VRPD optimally on a simulated small-scale problem and conduct a case study in one of the most affected regions by natural disasters. The numerical analysis demonstrates an improvement in the delivery time using three experiments that include testing the model on a set of benchmark problems and a case study based on the real scenario. The results show that the delivery time of the proposed model with the integration of three types of vehicle fleets can outperform the operation performed by a single-vehicle fleet by a significant percentage.

The global convergence of spectral RMIL conjugate gradient method for unconstrained optimization with applications to robotic model and image recovery.

In 2012, Rivaie et al. introduced RMIL conjugate gradient (CG) method which is globally convergent under the exact line search. Later, Dai (2016) pointed out abnormality in the convergence result and thus, imposed certain restricted RMIL CG parameter as a remedy. In this paper, we suggest an efficient RMIL spectral CG method. The remarkable feature of this method is that, the convergence result is free from additional condition usually imposed on RMIL. Subsequently, the search direction is sufficiently descent independent of any line search technique. Thus, numerical experiments on some set of benchmark problems indicate that the method is promising and efficient. Furthermore, the efficiency of the proposed method is demonstrated on applications arising from arm robotic model and image restoration problems.

Complementary surrogate-assisted differential evolution algorithm for expensive multi-objective problems under a limited computational budget

Different surrogate-assisted strategies can greatly influence the optimization efficiency of surrogate-assisted multi-objective evolutionary algorithms. By hybridizing two complementary surrogate-assisted strategies, this study proposed an efficient surrogate-assisted differential evolution algorithm to optimize expensive multi-objective problems under a limited computational budget. The two proposed surrogate-assisted strategies balance global and local search for multi-objective optimization. Specifically, one strategy is an improved surrogate-based multi-objective local search method that is based on maximin angle-distance sequential sampling. Compared with the previous local search method that is based on Euclidian distance-based sampling, the improved local search method is more efficient because it can mitigate the scale difference of different objectives. The other surrogate-assisted strategy is prescreening based on a diversity-enhanced expected improvement matrix infill criterion. The proposed infill criterion aims to improve the diversity of approximate Pareto optimal solutions by considering distribution of candidate individuals in the objective space in the infill function. Within a limited computational burden, the performance of the proposed algorithm is demonstrated on a large set of multi-objective benchmark problems, as well as a real-world airfoil design problem. Experimental results show that the proposed algorithm performs significantly better than some existing algorithms on most problems investigated in this study.

An Uncertainty Measure for Prediction of Non-Gaussian Process Surrogates.

Model management is an essential component in data-driven surrogate-assisted evolutionary optimization. In model management, the solutions with a large degree of uncertainty in approximation play an important role. They can strengthen the exploration ability of algorithms and improve the accuracy of surrogates. However, there is no a theoretical method to measure the uncertainty of prediction of Non-Gaussian process surrogates. To address this issue, this paper proposes a method to measure the uncertainty. In this method, a stationary random field with a known zero mean is used to measure the uncertainty of prediction of Non-Gaussian process surrogates. Based on experimental analyses, this method is able to measure the uncertainty of prediction of Non-Gaussian process surrogates. The method's effectiveness is demonstrated on a set of benchmark problems in single surrogate and ensemble surrogates cases.

The synchronized multi-assignment orienteering problem

<p style='text-indent:20px;'>We introduce the Synchronized Multi-Assignment Orienteering Problem (SMOP), a vehicle routing problem that requires jointly selecting a set of jobs while synchronizing the assignment and transportation of agents to roles to form ad-hoc teams at different job locations. Agents must be assigned only to roles for which they are qualified. Each job requires a certain number of agents in each role within a time window and contributes a reward score if selected. The task is to maximize the total reward attained. SMOP can model many real-world scenarios requiring coordinated transportation of resources and accommodates traditional depot-based workforces, depot workforces supplemented by ad-hoc workers, and fully ad-hoc workforces alike. The same problem formulation can be used for initial planning and mid-course replanning. We develop a mixed integer programming formulation (MIP) and an Adaptive Large Neighborhood Search algorithm (ALNS). In computational experiments covering a range of considerations, ALNS consistently found very near-optimal solutions on smaller problems and surpassed a commercial MIP solver substantially on larger problems. ALNS also found 24 new best solutions on a set of benchmark problems from the literature for the related Cooperative Orienteering Problem with Time Windows.</p>

Choose Appropriate Subproblems for Collaborative Modeling in Expensive Multiobjective Optimization.

In dealing with the expensive multiobjective optimization problem, some algorithms convert it into a number of single-objective subproblems for optimization. At each iteration, these algorithms conduct surrogate-assisted optimization on one or multiple subproblems. However, these subproblems may be unnecessary or resolved. Operating on such subproblems can cause server inefficiencies, especially in the case of expensive optimization. To overcome this shortcoming, we propose an adaptive subproblem selection (ASS) strategy to identify the most promising subproblems for further modeling. To better leverage the cross information between the subproblems, we use the collaborative multioutput Gaussian process surrogate to model them jointly. Moreover, the commonly used acquisition functions (also known as infill criteria) are investigated in this article. Our analysis reveals that these acquisition functions may cause severe imbalances between exploitation and exploration in multiobjective optimization scenarios. Consequently, we develop a new acquisition function, namely, adaptive lower confidence bound (ALCB), to cope with it. The experimental results on three different sets of benchmark problems indicate that our proposed algorithm is competitive. Beyond that, we also quantitatively validate the effectiveness of the ASS strategy, the CoMOGP model, and the ALCB acquisition function.

Cooperative Coevolution With Knowledge-Based Dynamic Variable Decomposition for Bilevel Multiobjective Optimization

Many practical multiobjective optimization problems have a nested bilevel structure in variables, which can be modeled as bilevel multiobjective optimization problems (BLMOPs). In this article, a cooperative coevolution (CC) with knowledge-based variable decomposition, called bilevel multiobjective CC (BLMOCC), is proposed for BLMOPs. In BLMOCC, the variable interactions are represented by an interaction matrix. The perturbation-based variable decomposition combined with the matrix completion approach has been designed for dynamically discovering the correlation among the bilevel variables, based on which the variables are divided into different groups. To further handle possible weak correlations among various groups of variables, a CC has been adopted for optimizing them in a collaborative way. In experimental studies, BLMOCC is compared with a nested method (NS) and a state-of-the-art algorithm (H-BLEMO) on a set of benchmark problems. The effects of each component in BLMOCC have also been verified by comparing it with its three variants. The experimental results demonstrate that BLMOCC has the best performance among all the compared algorithms. In addition, BLMOCC has also been applied to a real-world management decision-making problem, which further validates its efficiency and effectiveness.

A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics

We introduce a simple and general framework for the construction of thermodynamically compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems that satisfy an extra conservation law. As a particular example in this paper, we consider the general Godunov-Peshkov-Romenski (GPR) model of continuum mechanics that describes the dynamics of nonlinear solids and viscous fluids in one single unified mathematical formalism.A main peculiarity of the new algorithms presented in this manuscript is that the entropy inequality is solved as a primary evolution equation instead of the usual total energy conservation law, unlike in most traditional schemes for hyperbolic PDE. Instead, total energy conservation is obtained as a mere consequence of the proposed thermodynamically compatible discretization. The approach is based on the general framework introduced in Abgrall (2018) [1]. In order to show the universality of the concept proposed in this paper, we apply our new formalism to the construction of three different numerical methods. First, we construct a thermodynamically compatible finite volume (FV) scheme on collocated Cartesian grids, where discrete thermodynamic compatibility is achieved via an edge/face-based correction that makes the numerical flux thermodynamically compatible. Second, we design a first type of high order accurate and thermodynamically compatible discontinuous Galerkin (DG) schemes that employs the same edge/face-based numerical fluxes that were already used inside the finite volume schemes. And third, we introduce a second type of thermodynamically compatible DG schemes, in which thermodynamic compatibility is achieved via an element-wise correction, instead of the edge/face-based corrections that were used within the compatible numerical fluxes of the former two methods. All methods proposed in this paper can be proven to be nonlinearly stable in the energy norm and they all satisfy a discrete entropy inequality by construction. We present numerical results obtained with the new thermodynamically compatible schemes in one and two space dimensions for a large set of benchmark problems, including inviscid and viscous fluids as well as solids. An interesting finding made in this paper is that, in numerical experiments, one can observe that for smooth isentropic flows the particular formulation of the new schemes in terms of entropy density, instead of total energy density, as primary state variable leads to approximately twice the convergence rate of high order DG schemes for the entropy density.

Pro-Reactive Approach for Project Scheduling Under Unpredictable Disruptions.

Existing solution approaches for handling disruptions in project scheduling use either proactive or reactive methods. However, both techniques suffer from some drawbacks that affect the performance of the optimization process in obtaining good quality schedules. Therefore, in this article, we develop an auto-configured multioperator evolutionary approach, with a novel pro-reactive scheme for handling disruptions in multimode resource-constrained project scheduling problems (MM-RCPSPs). In this article, our primary objective is to minimize the makespan of a project. However, we also have secondary objectives, such as maximizing the free resources (FRs) and minimizing the deviation of activity finishing time. As the existence of FR may lead to a suboptimal solution, we propose a new operator for the evolutionary approach and two new heuristics to enhance the algorithm's performance. The proposed methodology is tested and analyzed by solving a set of benchmark problems, with its results showing its superiority with respect to state-of-the-art algorithms in terms of the quality of the solutions obtained.

Investigating the Correlation Amongst the Objective and Constraints in Gaussian Process-Assisted Highly Constrained Expensive Optimization

Expensive constrained optimization refers to problems where the calculation of the objective and/or constraint functions are computationally intensive due to the involvement of complex physical experiments or numerical simulations. Such expensive problems can be addressed by Gaussian process-assisted evolutionary algorithms. In many problems, the (single) objective and constraints are correlated to some extent. Unfortunately, existing works based on the Gaussian process for expensive constrained optimization treat the objective and multiple constraints as being statistically independent, typically for the ease of computation. To fill this gap, this article investigates the correlation among the objective and constraints. To be specific, we model the correlation amongst the objective and constraint functions using a multitask Gaussian process prior, and then mathematically derive a constrained expected improvement acquisition function that allows the correlation among the objective and constraints. The correlation between the objective and constraints can be captured and leveraged during the optimization process. The performance of the proposed method is examined on a set of benchmark problems and a real-world antenna design problem. On problems with high correlation amongst the objective and constraints, the experimental results show that leveraging the correlation yields improvements in both the optimization speed and the constraint-handling ability compared with the method that assumes the objective and constraints are statistically independent.

SOĞUK ZİNCİR LOJİSTİĞİNDE GEZGİN SATIN ALICI PROBLEMİ İÇİN İKİ AŞAMALI BİR ÇÖZÜM YÖNTEMİ

Bu çalışma, soğuk zincir lojistiğinde bozulabilir gıdaların satın alınması işlemini dikkate alarak literatürde iyi bilinen gezgin satın alıcı probleminin genişletilmiş bir halini sunmaktadır. Taşıma işlemlerinin bozulabilir ürün şartlarına dayalı gerçekleştirildiği bu problem, soğuk zincir lojistiğinde gezgin satın alıcı problemi (SZL-GSAP) olarak adlandırılmıştır. SZL-GSAP, sıcaklık kontrollü bir araç ile taşınması gereken çeşitli ürün taleplerinin belirli sayıda marketlerden satın alınması işlemini dikkate almaktadır. Problemin amacı, satın alıcı için sıcaklık kontrollü aracın enerji maliyetinin, ürün bozulma maliyetinin ve satın alma maliyetinin toplamını minimize edecek satın alma ve rota planını elde etmektir. Problem, doğrusal olmayan bir karma tamsayılı programlama modeli olarak formüle edilmiş ve iki aşamalı bir yöntem kullanılarak çözülmüştür. Çözüm yönteminin ilk aşamasında, bir çözüm kurucu yöntem kullanılarak problem için kaba bir sonuç elde edilmektedir. Daha sonra ilk aşamada elde edilen çözüm, GUROBI çözücüsü kullanılarak belirli bir zaman kısıtı içerisinde geliştirilmektedir. Sayısal uygulamalarda, önerilen çözüm yönteminin performansı, farklı büyüklükte örnekleri içeren bir problem seti üzerinde analiz edilmiştir.

A Hybrid Clustering Approach Based on Fuzzy Logic and Evolutionary Computation for Anomaly Detection

In this study, a new approach for novelty and anomaly detection, called HPFuzzNDA, is introduced. It is similar to the Possibilistic Fuzzy multi-class Novelty Detector (PFuzzND), which was originally developed for data streams. Both algorithms initially use a portion of labelled data from known classes to divide them into a given number of clusters, and then attempt to determine if the new instances, which may be unlabelled, belong to the known or novel classes or if they are anomalies, namely if they are extreme values that deviate from other observations, indicating noise or errors in measurement. However, for each class in HPFuzzNDA clusters are designed by using the new evolutionary algorithm NL-SHADE-RSP, the latter is a modification of the well-known L-SHADE approach. Additionally, the number of clusters for all classes is automatically adjusted in each step of HPFuzzNDA to improve its efficiency. The performance of the HPFuzzNDA approach was evaluated on a set of benchmark problems, specifically generated for novelty and anomaly detection. Experimental results demonstrated the workability and usefulness of the proposed approach as it was able to detect extensions of the known classes and to find new classes in addition to the anomalies. Moreover, numerical results showed that it outperformed PFuzzND. This was exhibited by the new mechanism proposed for cluster adjustments allowing HPFuzzNDA to achieve better classification accuracy in addition to better results in terms of macro F-score metric.

Testing Cyber–Physical Systems Using a Line-Search Falsification Method

Cyber-physical systems (CPSs) are complex and exhibit both continuous and discrete dynamics, hence it is difficult to guarantee that they satisfy given specifications, i.e., the properties that must be fulfilled by the system. Falsification of temporal logic properties is a testing approach that searches for counterexamples of a given specification that can be used to increase the confidence that a CPS does fulfill its specifications. Falsification can be done using random search methods or optimization methods, both of which have their own benefits and drawbacks. This article introduces two methods that exploit randomness to different degrees: 1) the optimization-free Hybrid-Corner-Random (HCR) and 2) the direct-search method Line-Search Falsification (LSF). HCR combines randomly chosen parameter values with extreme parameter values, which performs surprisingly well on benchmark evaluations. The gradient-free optimization-based LSF optimizes over line segments through a vector of inputs in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -dimensional parameter space. The two methods are compared to the Nelder-Mead and SNOBFIT methods, using a well-known set of benchmark problems and LSF shows better performance than any of the evaluated methods.

Chebfun Solutions to a Class of 1D Singular and Nonlinear Boundary Value Problems

The Chebyshev collocation method implemented in Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for tough problems, we have to loosen the default Chebfun tolerance in Newton’s solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic, the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how the Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).

Meta-Optimization of Dimension Adaptive Parameter Schema for Nelder–Mead Algorithm in High-Dimensional Problems

Although proposed more than half a century ago, the Nelder–Mead simplex search algorithm is still widely used. Four numeric constants define the operations and behavior of the algorithm. The algorithm with the original constant values performs fine on most low-dimensional, but poorly on high-dimensional, problems. Therefore, to improve its behavior in high dimensions, several adaptive schemas setting the constants according to the problem dimension were proposed in the past. In this work, we present a novel adaptive schema obtained by a meta-optimization procedure. We describe a schema candidate with eight parameters subject to meta-optimization and define an objective function evaluating the candidate’s performance. The schema is optimized on up to 100-dimensional problems using the Parallel Simulated Annealing with Differential Evolution global method. The obtained global minimum represents the proposed schema. We compare the performance of the optimized schema with the existing adaptive schemas. The data profiles on the Gao–Han modified quadratic, Moré–Garbow–Hilstrom, and CUTEr (Constrained and Unconstrained Testing Environment, revisited) benchmark problem sets show that the obtained schema outperforms the existing adaptive schemas in terms of accuracy and convergence speed.

A Stigmergy-Based Differential Evolution

Metaheuristic algorithms are techniques that have been successfully applied to solve complex optimization problems in engineering and science. Many metaheuristic approaches, such as Differential Evolution (DE), use the best individual found so far from the whole population to guide the search process. Although this approach has advantages in the algorithm’s exploitation process, it is not completely in agreement with the swarms found in nature, where communication among individuals is not centralized. This paper proposes the use of stigmergy as an inspiration to modify the original DE operators to simulate a decentralized information exchange, thus avoiding the application of a global best. The Stigmergy-based DE (SDE) approach was tested on a set of benchmark problems to compare its performance with DE. Even though the execution times of DE and SDE are very similar, our proposal has a slight advantage in most of the functions and can converge in fewer iterations in some cases, but its main feature is the capability to maintain a good convergence behavior as the dimensionality grows, so it can be a good alternative to solve complex problems.

A multi-objective bilevel optimisation evolutionary algorithm with dual populations lower-level search

In multi-objective bilevel optimisation problems, the upper-level performance of different lower-level optimal solutions may be very different, even though they belong to the same lower-level problem. It may lead to poor optimisation results. Therefore, the lower-level search should search lower-level non-dominated solutions that are also non-dominated in the upper-level objective space. In this paper, we use two populations in the lower-level search. The first population maintains non-dominance and diversity in the lower-level objective space and provides the second population with convergence pressure from the lower level. The second population selects the upper-level non-dominated solutions that are not dominated by the first population in the lower-level objective space, which make the second population maintain the non-dominance at both upper and lower levels. Besides, to improve the search efficiency, we set up the upper-level mating pool to generate the upper-level vectors of offsprings near the upper-level vectors of the better individuals in the current population. To balance convergence and diversity, the selection operator of a decomposition based multi-objective evolutionary algorithm is adopted. The proposed algorithm has been evaluated on a set of benchmark problems and a real-world optimisation problem. Experimental results demonstrate that the proposed algorithm is efficient and effective.